When do trajectories matter? Identifiability analysis for stochastic transport phenomena

TL;DR

This paper analyzes when trajectory data improves parameter identifiability in stochastic diffusion models, showing that combining count and trajectory data enhances inference and experimental design.

Contribution

It introduces a comprehensive framework combining simulations, PDEs, and likelihood methods to assess data types' impact on model parameter identifiability.

Findings

Count data alone can cause structural non-identifiability issues.

Trajectory data can alleviate non-identifiability in diffusion models.

Different data collection protocols influence the precision of parameter inference.

Abstract

Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across a range of scales, including count data collected across a series of fixed sampling regions to characterize population-level dispersal, as well as individual trajectory data to examine at the motion of individuals within a diffusive population. In this work we consider a lattice-based random walk model and examine the extent to which model parameters can be determined by collecting count data and/or trajectory data. Our analysis combines agent-based stochastic simulations, mean-field partial differential equation approximations, likelihood-based estimation, identifiability analysis, and model-based prediction. These combined tools reveal that working with count data alone can sometimes lead to challenges involving structural non-identifiability that can be alleviated by collecting trajectory data. Furthermore, these tools allow us to explore how different experimental designs impact inferential precision by comparing how different trajectory data collection protocols affects practical identifiability. Open source implementations of all algorithms used in this work are available on GitHub.